Mirroring to create a single polygon across the mirroring plane
The mirror modifier in your illustration is working exactly as it is designed to do. In this case, it is mirroring an edge. To complete a face, you need to add one more vertex, located at the intersection of a line perpendicular to the y axis, and the y axis, which passes through the vertex furthest from the y axis, and create the face. The easiest way to create this vertex in the illustrated figure is to extrude from the vertex at the far right to the y axis, constraining the extrusion to the x direction. If you do this, the mirror modifier will work the way you wish.